Question

Given that m angle G- 81", what is m angle I?
A)81"
B)89
C)91
D)99

Answer 1

The answer to the question is D)99

Answer 2

`\text{D) }99^(\circ)`

Explanation:

Define a cyclic quadrilateral by a quadrilateral that is circumscribed by a circle. In this case, since the quadrilateral shown is circumscribed by a circle, it is a cyclic quadrilateral.

A property of all cyclic quadrilaterals is that their opposite angles are supplementary, meaning they add up to 180 degrees. Since
`\angle G` and
`\angle I` are opposite angles in the quadrilateral, they must be supplementary. Therefore, we have the equation:

`\angle G+\angle I=180,\\81^(\circ)+\angle I=180,\\\angle I=180-81=\boxed{99^(\circ)}`